When did the music die? And why? It will be 30 years in August since the death of Dmitri Shostakovitch. Next year also marks the 30th anniversary of the death of Benjamin Britten. Aaron Copland, older than both of them, lived on until 1990 and Olivier Messiaen until 1992. But apart from these?

I can see them already. The protestations on behalf of the half-forgotten and semi-famous, the advocates of Henze and Berio, the followers of Tavener and Adès. Perhaps there will be a good word for Golijov or Gubaidulina, for Piazzola or Saariaho (enthusiasms I share). And maybe, even now, there remains someone who believes that Stockhausen should be mentioned in the same breath as Bach, the last of the true believers clinging to the shipwreck of modernism.

Whatever happened to the composers? Last Saturday, the BBC relayed a broadcast from New York of Puccini's Turandot, the opera featuring the most famous aria of them all, Nessun Dorma. Yet Turandot, left unfinished on the composer's death in 1924, is also the grand finale of Italian opera. For around three centuries, operas poured from the pens of Italian composers and found lasting places in the repertoire. After Turandot, there has not been one in 80 years of which that could be said.

Maybe that is an extreme example. But answer this question: what is the most recently composed piece of classical music to have achieved a genuinely established place in the repertoire? I mean a piece that you can count on hearing in most major cities most years, and a performance of which is likely to bring in a large general audience. Shostakovich's first cello concerto, written in 1959, perhaps? Even that is stretching a point. A more truthful answer might be Richard Strauss's Four Last Songs, composed 56 years ago in 1948.

And you think this is conservative? Then how about these conclusions, which come from a marvellously stimulating new book by the South African scholar Peter Van der Merwe*. He reckons that by 1939, the year of Rodrigo's Concierto de Aranjuez, the flow of music that is both genuinely modern and popular had all but dried up. Van der Merwe nods towards Khachaturian, late Strauss and the Britten of Peter Grimes - and, er, that's it. For the general public, he argues, classical music ceased to exist by 1950.

There will be an interesting argument about when and where the line can be drawn. That it can be drawn somewhere (1940, 1950 or 1960 hardly matters) is, however, beyond serious dispute. At some point in the past half-century, classical music lost touch with its public.

At the start of the 21st century, we can see what went wrong more clearly. What went wrong was western European modernism. Modernism is a huge, varied and complex phenomenon, and it took on different qualities in different national cultures. But an essential feature, especially as Van der Merwe argues it, was to turn music decisively towards theory - often political theory - and away from its popular roots.

The pioneer figure was Arnold Schoenberg, with his theory of the emancipation of dissonance (which, as Van der Merwe cleverly points out, also implied the suppression of consonance). But it was after Schoenberg's death, in the period 1955-80, that his ideas achieved the status of holy writ.

The upshot was a deliberate renunciation of popularity. The audience that mattered to modernists (even the many who saw themselves as socialists) ceased to be the general public and increasingly became other composers and the intellectual, often university-based, establishment that claimed to validate the new music, not least through its influence over state patronage. Any failure of the music to become popular was ascribed not to the composer's lack of communication but the public's lack of understanding.

Not surprisingly, the public looked elsewhere, to what we are right to call, and right to admire for being, popular music. This embrace started in the early 20th century with ragtime and jazz and reached its apex with rock'n'roll, whose great years belong to that same period, 1955-80, when modernism ruled in the academy. Today, public taste and knowledge are more eclectic than ever. The news that Oasis are to be part of the GCSE music syllabus reflects that, as does Radio 3's march into world music.

Classical music survived, after a fashion. But it has less to say about today. It endures overwhelmingly on the strength of its back catalogue and performance tradition, not of any new creativity. Having failed to persuade the public to embrace modern music, it has sustained itself only by rediscovering the music of earlier epochs and - though this is arguable - by learning the lessons of the modernist deviation.

This has left the traditional carriers of the classical tradition in steady, though not yet terminal, decline. Orchestras and opera companies battle on in the face of increasing evidence of public indifference and of diminishing investment. Solo performers remain of a high standard, but sound less and less like the bearers of a living tradition.

In the latest issue of Prospect magazine, the Philharmonia Orchestra's managing director, David Whelton, observes that we inhabit "a period where the broad population of this country is totally unfamiliar with orchestral music". If you schedule the New World symphony, he reckons, half the audience will be hearing this once familiar work for the first time.

So is it goodbye to all that? Not necessarily. The modernist tide has gone out, though parts of western Europe are still mopping up. Even here, though, it is no longer anathema for composers to embrace popularity. The influence of American composers, for whom popularity is not a dirty word, and of composers from national traditions that survived the modernist onslaught (the Argentinian school, for instance) is perhaps a way forward. Van der Merwe, for one, believes that it is.

Classical music's second coming, if it is to have one, could hardly be better timed. The popular music that once filled the place it vacated seems in turn to have largely burned itself out. Here, too, creativity is at its lowest ebb since the early 50s. The space awaiting good new music of any kind is immense.

But at least classical music has come up for air, and is asking the right questions. This is more than can be said of some of the visual arts, where the dislike of the public remains as striking and juvenile as ever. Even this, though, will not last. The need to create something beautiful that excites the public and goes beyond its experience is too strong to be frustrated indefinitely. It would just be nice to think it might resume in our lifetime.

*Roots of the Classical: the Popular Origins of Western Music, by Peter Van der Merwe (OUP)